The new isotopes247Md,243Fm,239Cf,and investigation of the evaporation residues from fusion of206Pb,208Pb,and209Bi with40Ar

The evaporation residues produced in heavy ion fusion reactions between⁴⁰Ar and²⁰⁶Pb,²⁰⁸Pb, and²⁰⁹Bi, respectively, were investigated. They were separated in-flight using a velocity filter (SHIP) and identified after implantation into an array of position sensitive surface barrier detectors by measuring their decay characteristics. Three newα-emitting isotopes were found:²⁴⁷Md,²⁴³Fm, and²³⁹Cf.²⁴⁷Md was identified by correlation to its known daughter decay²⁴³Es, and²⁴³Fm and²³⁹Cf were observed as correlated decays. Moreover, all previously known deexcitation channels, characterized by spontaneous fission or byα decay, could be observed for the first time in one experimental setup. Our results for formation cross sections and decay characteristics are in agreement with known data.     

Gamma-ray yields from 12C + 13C reactions near and below the coulomb barrier

The γ-ray yields from low-lying transitions in heavy residual nuclei produced in the ¹²C+¹³C reaction have been measured from E_c.m. = 3.1 to 11.9 MeV using a Ge(Li) detector. Total cross sections for compound nucleus formation were deduced from the experimental data with the aid of the Hauser-Feshbach model. Several independent checks on this procedure are described. These tests verify the assumptions made in the analyses of this reaction and suggest that the deduced cross sections have an absolute uncertainty of ±30 %. The present experimental results for the ¹²C+¹³C reaction are qualitatively very different from those for the ¹²C+¹²C reaction and do not provide any striking evidence for either broad singleparticle resonances in the total reaction cross section or for narrow non-statistical (quasimolecular) resonances in summed cross sections for proton and for α-particle emission to bound states of ²⁴Na and ²¹Ne, respectively. The predictions of several optical models employing attractive nuclear potentials are compared to the data. None is successful in reproducing the measured cross sections over the entire range of bombarding energy. The predictions at low energies depend sensitively on the shape of the potential a few fm inside the region of the nuclear surface. A narrow, rapidly varying energy dependence of the γ-ray yields is observed, with a peak-to-valley ratio of typically 1.1. However, a statistical analysis shows that these fluctuations, and those observed in recent charged particle measurements of α-particle yields, are reasonably consistent with those expected from the formation and decay of strongly overlapping levels in the compound nucleus. Finally, several observations are made on the validity of certain approximations often made in statistical analyses of heavy-ion reactions.     

Evidence for quasi-fission in40Ar+208Pb collisions near the coulomb-barrier

Fission-fragment angular distributions were measured in the reaction of⁴⁰Ar with²⁰⁸Pb near the fusion barrier. For nearly symmetric mass-/charge splits we find angular distributions symmetric around θ=90 degrees, however, with unusually large anisotropies. These develop gradually into forward-backward asymmetric distributions as one moves away from mass-/charge symmetry. This indicates that non-compound fission (‘quasi-fission’) competes with true fusion-fission. The relative contribution of quasi-fission to the total fission cross section is somewhere between 51 and 85%. In the framework of the extra-push model this is equivalent to an extra-extra push energy for compound-nucleus formation inside the true fission saddle point of 4<E _xx <9 MeV in agreement with a recent empirical parametrization of fusion-barrier shifts based on fusion-fission cross sections. On the basis of cross sections for fusion-evaporation residues it had previously been concluded that fusion of⁴⁰Ar with Pb isotopes occurs unhindered. Possible reasons for this apparent discrepancy are discussed.     

Inelastic scattering and nucleon transfer in the system232Th+206Pb near the Coulomb barrier

Nucleon transfer accompanied by Coulomb excitation was studied in the system²⁰⁶Pb+²³²Th atE _Lab=6.4 MeV/u. Particle-particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and nucleon transfer reactions. The mean excitation energy was measured by means of aγ-ray energy and multiplicity filter consisting of 6 NaI detectors. Large cross sections for one-neutron and two-neutron pick-up from²³²Th are observed. The impact-parameter dependence of the neutron transfer is analyzed in terms of semiclassical barrier penetration models. Using realistic neutron potentials with a diffuse surface, the experimental data are in accordance with the assumption of a “cold” transfer to states near the yrast line.     

Transfer, breakup, and fusion reactions of 6He with 209Bi near the Coulomb barrier

The fusion of ⁶He with a ²⁰⁹Bi target displays a large enhancement at energies near to and below the Coulomb barrier. Recently, a ⁴He group of remarkable intensity, which dominates the total reaction cross-section, has also been observed in the near-barrier interaction of the same system. It is argued that this transfer/breakup channel acts as a doorway state to fusion. Received: 1 May 2001 / Accepted: 4 December 2001     

The reaction Rb(d,p)Rb near the coulomb barrier

Cross sections for the reaction ⁸⁷Rb(d, p)⁸⁸Rb induced by 4 to 6 MeV deuterons were measured to obtain spectroscopic data on levels in ⁸⁸Rb. The Q-value for the reaction to the ground state of ⁸⁸Rb was 3.837 ± 0.020 MeV. In addition twenty-three levels up to 3 MeV excitation in ⁸⁸Rb were populated. Four different deuteron optical model parameter sets, which fit our ⁸⁷Rb(d, d) elastic scattering data, were used in a DWBA analysis. Assignments of l_n, were made to nine levels on the basis of angular distribution shapes and excitation functions. Relative spectroscopic factors were determined with a maximum deviation of only 15%. However absolute spectroscopic factors were extremely sensitive to the neutron radius parameter, and hence the normalization of the bound neutron wave functions. The structure of ⁸⁸Rb is discussed.     

Activation cross sections for reactions of 109Ag induced with 40Ar ions

Activation cross sections for reactions of enriched targets of ¹⁰⁹Ag with ⁴⁰Ar ions of 288 and 228 MeV have been determined by γ-ray spectroscopy. Yields of evaporation residues and low-mass transfer products have been measured. Evaporation residue yield-mass distributions are compared with three sets of statistical model results. The calculation based on a rotating liquid drop model with fission competition is in very good agreement with experimental results. It is shown that the yields are inconsistent with a mechanism of incomplete fusion plus evaporation.     

The finite size effects in fusion of deformed nuclei at incident energies near the barrier

By the end of the last century, the precision of heavy-ion-fusion cross-section measurement had been increased up to 1%. This allowed the measured cross sections to be converted into experimental fusion-barrier distributions. In the experimental analysis, the barrier distributions were analyzed using a Woods-Saxon shape for the nuclear part of the bare nucleus-nucleus potential. This potential was defined along the line joining the centers of the two nuclei (“centerline potential”), which, for deformed nuclei, contradicts the short-range character of the nucleon-nucleon (N N) nuclear interaction. We present the results of our theoretical study of the significant deviations of the simplified potential from a “realistic” nuclear potential. The finite-size effects on the potential for deformed nuclei were first investigated in an approximate geometrical way. Then a more rigorous approach, namely, a semimicroscopic double-folding model, was applied to calculate the nucleus-nucleus potential. The angle-dependent fusion barriers calculated with a simple delta-function-like exchange term of the N N M3Y interaction was found to be very similar to those calculated with a finite-range expression. This circumstance enables us to perform rather quick calculations of the fusion cross sections and the corresponding barrier distributions. Comparison of the results with the experimental data showed that the finite-size effects are substantial and cannot be ignored in a quantitative analysis of experimental fusion cross sections and barrier distributions. The text was submitted by the authors in English.     

Rotational energy and limits to fusion reactions between two nuclei

The energy balance of the fusion process between two nuclei is discussed with respect to the rotational energy. Two energy regimes are obtained. In the first regime the increase of rotational energy of the compound system as function of incident energy is governed by the moment of inertia of the two-fragment system at the barrier configuration. The faster increase of rotational energy of the compound system is furnished by theQ-value. In a sliding collision only part of theQ-value can be converted into rotational energy. Therefore, the Yrast limit in the population of the compound nucleus cannot be reached. When this source of energy is exhausted at a certain angular momentum, a second regime is obtained; then the increase of angular momentum and rotational energy as function of incident energy must be determined by the moment of inertia of the compound system.     

Inelastic electron scattering from low-lying states in the nuclei 36Ar and 40Ar

The low-lying level structure of ³⁶Ar and ⁴⁰Ar has been investigated using the technique of inelastic electron scattering. Data were collected at the National Bureau of Standards Linear Accelerator with incident electron energies between 65 and 115 MeV and scattering angles of 92.5° and 110°. The data span a range of momentum transfer squared between 0.29 and 0.92 fm^?2. Tassie model and Helm model analyses have been applied to data for levels at 1.97 and 4.18 MeV in ³⁶Ar and at 1.46, 2.52, 3.21 and 3.68 MeV in ⁴⁰Ar. A 2⁺ assignment to the 3.21 MeV state in ⁴⁰Ar is suggested. Transition strengths, transition radii, and mean lifetimes for these states are computed and compared with results of previous experiments.     

Excitation functions of fusion reactions and neutron transfer in the interaction of 6He with 197Au and 206Pb

Excitation functions for evaporation residues in the reactions ¹⁹⁷Au(⁶He, xn)^203-xnTl, x = 2-7, and ²⁰⁶Pb(⁶He, 2n)²¹⁰Po, as well as for neutron transfer reactions for the production of ¹⁹⁶Au and ¹⁹⁸Au in the interaction of ⁶He with ¹⁹⁷Au were measured. The ⁶He beam was obtained from the accelerator complex for radioactive beams DRIBs (JINR). The maximum energy of the beam was about 10AMeV and the intensity reached 2×10⁷pps. The stacked-foil activation technique was used directly in the beam extracted from the cyclotron or in the focal plane of the magnetic spectrometer MSP-144. The identification of the reaction products was done by their radioactive γ- or α-decay. The fusion reaction with the evaporation of two neutrons was characterized by an increase in the cross-section compared to statistical model calculations. The analysis of the data in the framework of the statistical model for the decay of excited nuclei, which took into account the sequential fusion of ⁶He has shown good agreement between the experimental and the calculated values of the cross-sections in the case of sub-Coulomb-barrier fusion in the ²⁰⁶Pb + ⁶He reaction. An unusually large cross-section was observed below the Coulomb barrier for the production of ¹⁹⁸Au in the interaction of ⁶He with ¹⁹⁷Au. Possible mechanisms of formation and decay of transfer reaction products are discussed.     

Fusability and fissionability in 86Kr-induced reactions near and below the fusion barrier

Evaporation-residue excitation functions for the reactions ⁸⁶Kr + ^70,76Ge, ^92,100 Mo, ^99,102,104 Ru have been measured using activation methods and the velocity filter SHIP. The data span the region from well below the fusion barrier up to, and beyond, the energy where limitation by fission competition takes place. The data are shown to be compatible with the concept of complete fusion followed by the statistical decay of the equilibrated compound nucleus. Information on both the fusion probability at and below the fusion threshold and the fissionability of the compound nuclei formed, is extracted. The model dependence of the extracted fission barriers is discussed in detail. In analogy to studies involving lighter projectiles, strong correlations between the low-energy nuclear-structure properties of the nuclei and the subbarrier fusion probability are found. A relative shift of the fusion barrier to higher energies, that increases with the number of valence neutrons in the target nuclei, is observed.     

Sub and near barrier fusion of neutron rich heavy nuclei – studies with radioactive ion beams

The availability of accelerated fission fragments at HRIBF allows us to study fusion reactions where one of the reactants is a short-lived exotic nucleus. Most interesting in this respect are entrance channels involving neutron-rich target and projectile – where enhanced survival probability of the compound system may allow the synthesis of heavier system. Much depends though on the dynamic evolution of the captured nuclei into a compound nucleus and the ensuing competition between fission and evaporation residue decay modes. Our studies of fusion between heavy neutron-rich nuclei are aimed at acquiring data that will lead to the understanding and eventually the ability to predict the probabilities for these different processes.     

Transfer and fusion reactions of unstable nuclei

The transfer and fusion reactions are studied for reactions between a stable and an unstable nucleus with neutron skin, taking as examples the reactions ^16,28O+⁴⁰Ca. The two-dimensional time-dependent Hartree-Fock method is used. It is shown that, in such reactions, the nucleon transfer is enhanced enormously for both protons and neutrons. The neutron skin does not enhance the fusion cross section contrary to the usual expectation.     

A study of the reactions208Pb(d,d)208Pb and208Pb(d,p)209Pb at energies above and below the Coulomb barrier

The reactions²⁰⁸Pb(d, d)²⁰⁸Pb and²⁰⁸Pb(d, p)²⁰⁹Pb have been studied in the energy region from below to above the Coulomb barrier. An optical-model analysis of the elastic scattering results has been performed to obtain parameters for a DWBA analysis. Distorted wave calculations for the direct transitions leading to single-particle states in²⁰⁹Pb have been used to extract spectroscopic factors. Only two deuteron potential sets give a good account of the stripping data throughout the energy region studied.     

Production cross sections for the heaviest nuclei in complete fusion reactions induced by heavy ions

Production of the heaviest nuclei in complete fusion reactions induced by heavy ions has been considered in a systematic way in the framework of the conventional barrier passing model coupled with the statistical model. Available data on excitation functions for fission and production of evaporation residues (ER) in very asymmetric combinations induced by ions lighter than Ne on actinide target nuclei are described rather well in the framework of these models. The data allow one to adjust model parameters and to reveal the quasi-fission effect caused by the interaction with deformed target nuclei, which is manifested in the suppression of the ER production at sub-barrier energies. For reactions induced by Mg and heavier projectiles, quasi-fission is starting to suppress fusion (ER production) at energies above the Coulomb barrier. One has to introduce empirically the quantity of the fusion probability P_fus to reproduce the ER excitation functions in the framework of the conventional approach. The exponential dependence of P_fus on the combined fissility parameter (a similar parameter that was introduced for the extra-push energy scaling) was found in search for scaling for the P_fus values resulting from the data analysis.     

Competition between binary reactions and fusion in heavy-ion collisions at the Coulomb barrier

Mass and charge distributions for binary reaction channels have been measured for the reactions⁸⁶Kr with⁷⁶Ge,¹⁰⁴Ru and¹³⁰Te at the Coulomb barrier using chemical separations and-ray spectroscopy. These systems span the region where dynamical hindrance to complete fusion sets in. The binary reactions can be subdivided into two components associated withi) reflection from the outer potential barrier (quasielastic), andii) reseparation after passing the barrier (complex reactions). The sum of complex-reaction channels and evaporation residues from complete fusion can be reproduced by a barrier passing calculation. The fraction of the barrier passing flux leading to reseparation increases from 26±10% for the lightest system to more than 90% for the heaviest system. The data indicate that fusion hindrance is primarily caused by reseparation shortly after passage of the barrier before Swiatecki's conditional saddlepoint is overcome, resulting in partitions close to the entrance channel configuration. In addition, for the heaviest system, a quasifission component representing somewhat less than 20% of the barrier-passing flux was observed. From the missing masses of fragment pairs we can deduce that the reseparating complex-reaction products have kinetic energies well below the fusion barrier and share the excitation energy in a way similar to the sawtooth-like curve known from low-energy fission. The quasielastic, predominantly one- and two-nucleon transfer channels, have strongly varying cross sections for the three systems despite similar effectiveQ-values. A systematics of one-neutron transfer cross sections at the Coulomb barrier is established and shown to differ considerably from the smooth behaviour observed at energies 20–30% above the barrier. The connection to nuclear polarization phenomena and orbit matching is pointed out.Nuclear reactions:⁷⁶Ge,¹⁰⁴Ru,¹³⁰Te(⁸⁶Kr, X).E=3.22 MeV/u, (3.64) 3.84 MeV/u, 3.96 MeV/u; enriched targets; catcher foil technique, chemical separations,-ray spectroscopy; deduced mass and charge distributions for binary reactions; competition with complete fusion